This invention relates to removing noise from the digitized output of a sensor, the sensor being subject to undesired (although perhaps necessary) internal or external resonance. It further relates to such removal when the resonant frequency is unknown or drifts.
A popular form of angular rate sensor includes a piezoelectric tuning fork. When the fork is rotated, coriolis forces distort the fork proportionally to the magnitude of the rotation. Effects of resonance of the tuning fork, however, must be removed from the output signal from the fork. This is possible, with a notch filter, if the effect is at a frequency removed from the frequency of interest by an order of magnitude. This is often the case.
In the foregoing example, the resonance is internal to the sensor. It is equally desirable to remove resonance-induced noise from the output of a sensor even when the resonance is external to the sensor. This would occur, for example, in electrical equipment powered by an unstable supply. 60-cycle hum from commercially supplied electricity is easily notched out, but the unstable output of an emergency generator can make its way into a signal to be measured, and is much more difficult to remove. Again, the resonant frequency (and its effect) must be at a frequency somewhat removed from the frequency of interest.
We return to the angular rate sensor with an underlying operating frequency which must be removed from its output signal. This removal is relatively straightforward with a (digital) stagger-tuned notch filter when the frequency range is somewhat known. Stagger-tuned notch filters, however, introduce considerable phase lag.
When the frequency is grossly unknown, unstable, or both, stagger-tuned filters introduce so much phase lag--even at frequencies at some distance below the notch frequency--as to make them unsuitable for an important application: closed-loop control. The solution is to use a very narrow adaptive notch filter, the very narrowness of which greatly reduces phase lag. However, a very narrow notch filter must be an infinite impulse response (IIR) filter; it must be recursive. This in turn makes the adaptive tracking of the notch frequency of the filter unstable: there are many relative minima on the performance-criterion surface. This in turn makes it unsuitable for closed-loop control.
What is needed is an IIR filter to notch out the objectionable resonance with the stable adaptive properties of a non-recursive, finite impulse response (FIR) filter. This problem seems insoluble.